Show that the sequence defined by 1 a₁ = 1 an is increasing and an < 3 for all n. Deduce that {an} is convergent and find its limit. = 3 an+1 -

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.1: Infinite Sequences And Summation Notation
Problem 72E
icon
Related questions
Question
Show that the sequence defined by
1
a1 = 1
an+1 = 3
an
is increasing and an < 3 for all n. Deduce that {an} is convergent and find
its limit.
Transcribed Image Text:Show that the sequence defined by 1 a1 = 1 an+1 = 3 an is increasing and an < 3 for all n. Deduce that {an} is convergent and find its limit.
Expert Solution
steps

Step by step

Solved in 3 steps with 3 images

Blurred answer
Similar questions
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
College Algebra
College Algebra
Algebra
ISBN:
9781938168383
Author:
Jay Abramson
Publisher:
OpenStax